Properties Of Determinants and Matrices for CBSE Class 12

We are already familiar with what determinants are. We know that for every square matrix \( [A]_{n×n}\) there exists a determinant to the matrix such that it represents a unique value. In the upcoming discussions, we will learn about certain properties of determinants which simplify the calculation of the determinant.

1. Property of Reflection:

If in a determinant, even when rows are interchanged with columns, the value of the determinant remains unaltered.

5. Property of multiplication by a Scalar:

If all the elements of a row or a column in a determinant are multiplied by a constant non-zero value then the value of the determinant also becomes a multiple of that constant i.e. If \(\triangle =\begin{vmatrix} a & kb & c\cr d & ke & f\cr g & kh & i \end{vmatrix}\).

There you go!! These are the basic properties of determinants and we are sure you want to learn more. To know more about different concepts like matrices and determinants across different subjects download BYJU’S-The Learning App.

Practise This Question

Pavan drew two lines and he measured some angles. He found that ∠1=∠5 and so he concluded that the two lines are parallel.

Practise This Question

Kushagra is drawing a railway track on paper as a part of his project. He asked Sarosh to draw a line parallel to the given line. Sarosh said that we can only construct a line parallel to the given line using alternate angles concept. Is this true?